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Mathematics > Geometric Topology

Title:Hom Quandles

Abstract: If $A$ is an abelian quandle and $Q$ is a quandle, the hom set
$\mathrm{Hom}(Q,A)$ of quandle homomorphisms from $Q$ to $A$ has a natural
quandle structure. We exploit this fact to enhance the quandle counting
invariant, providing an example of links with the same counting invariant
values but distinguished by the hom quandle structure. We generalize the result
to the case of biquandles, collect observations and results about abelian
quandles and the hom quandle, and show that the category of abelian quandles is
symmetric monoidal closed.